Consider a principal-agent problem with three exogenous states of nature, θ_1,,θ_2,θ_3, two effort levels, e_L...

   Consider a principal-agent problem with three exogenous states of nature, θ_1,,θ_2,θ_3, two effort levels, e_L and e_H and two output levels, distributed as follows as a function of the state of nature and the effort level:
State of Nature   θ_1   θ_2   θ_3
Probability   1/4   1/2   1/4
Output under e_H   18   18   1
Output under e_L   18   1   1
The principal is risk neutral, while the agent has utility function u(w)=w^(1/2). when receiving monetary compensation w, minus the cost of effort, which is normalized to 0 for e_L and to 0.1 for e_H. The agent’s reservation expected utility is 0.1.
   Derive the first-best contract.

Derive the second-best contract when only output levels are observable.

Assume the principal can buy for a price 0.1 an information system that allows the parties to verify whether state of nature θ_3 happened or not. Will the principal buy this information system? Discuss.

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orchestra answered 2 years ago

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